mysterious fish losses

[Aquamarina]

More answers to above questions (having calmed down a bit!):
-I previously have used no additives at all, except what might be in the Instant Ocean salt
-Water changes, up to this month, were 10% once monthly and seemed to be sufficient. I have done 5-10% changes after each death. I thought the newly mixed salt water had to sit for a week before it could be used...?
-Water temp is in normal bounds (now 81.2), although this week I have reduced the amount of time the lights are on, because the house became warmer.
-No new fish have been added for many months. On the shop person's recommendation, I did add one small live rock this week, as all the rock in the tank is lava stone.
-As mentioned, the protein skimmer was not working properly for awhile, and I was busy adjusting the flow every week, not realizing the pump was defective. The new pump was installed on May 16 (the tower looked pretty clean), and I have cleaned it again today with tap water only.
-Other filtration: bio balls
-Fish food is frozen cubes Hikari/Kyorin of various sorts (Mysis shrimp, plankton, mega marine algae/angel, squid, bloodworms). I feed a selection of each once daily: eg. 4 small cubes for 10 fish (butterfly, 3 yellow tangs, trigger, clown, tomato clown, blue damsel, zebra damsel, cowfish). They seem to eat all the food in 5 minutes. Occasionally, I give them nori.